Bond Yield Calculator Guide: YTM, Coupon & Duration债券收益率计算器指南：到期收益率、票面利率与久期
Bonds look simple on the surface — you lend money, you get coupons, you get your principal back at the end. But the relationship between the price you pay, the coupon you receive, and the yield you actually earn is anything but obvious. This guide walks through the three numbers that matter (coupon rate, current yield, yield to maturity), the price-yield inverse relationship, and why duration matters more than maturity when rates move.
What Is a Bond?
A bond is a loan you make to a government or corporation. In return, the issuer promises two things: regular interest payments (called coupons) and the return of your original principal (the face value) at a fixed future date (the maturity date). A 10-year Treasury with a 4% coupon, for example, pays you $40 per year per $1,000 of face value, then returns the $1,000 at the end of year 10.
Bonds are quoted as a percentage of face value. A bond "at 100" trades at face value; "at 95" trades at a 5% discount; "at 105" at a 5% premium.
Coupon vs Yield — Three Numbers
The bond world is confusing because there are three yield figures, each measuring something different:
- Coupon rate — the fixed interest payment as a percent of face value. Set at issuance, never changes.
- Current yield — annual coupon divided by the current price. Tells you the cash income from holding the bond today.
- Yield to maturity (YTM) — the total return if you buy at today's price and hold to maturity. Includes coupons and the gain or loss when the bond is redeemed at face value.
YTM is the only number that lets you compare bonds at different prices and coupons on equal footing.
The YTM Formula
YTM is the discount rate that makes the present value of all future cash flows equal the current price:
- P — current bond price
- C — coupon payment per period
- y — yield per period (YTM ÷ periods per year)
- FV — face value redeemed at maturity
- n — total periods remaining
There is no closed-form solution; YTM is solved iteratively (Newton-Raphson or a financial calculator).
Worked example: a 5-year bond with a 5% annual coupon (so $50/year on a $1,000 face) trading at $950. Solve for y in:
950 = 50/(1+y) + 50/(1+y)² + 50/(1+y)³ + 50/(1+y)4 + 1050/(1+y)5 → y ≈ 6.0%
YTM is higher than the coupon (6.0% vs 5.0%) because you bought at a discount — you get back $1,000 face value, which is $50 more than you paid.
The Inverse Price-Yield Relationship
When market interest rates rise, the price of existing bonds falls. When rates fall, prices rise. The reason: a 5% coupon becomes less attractive when new bonds are paying 6% — so the only way to convince someone to buy the older bond is to drop its price.
| Market yield | 5% coupon bond price | Capital gain/loss at maturity |
|---|---|---|
| 4% | ≈ $1,045 (premium) | −$45 loss |
| 5% | = $1,000 (par) | $0 |
| 6% | ≈ $958 (discount) | +$42 gain |
| 7% | ≈ $918 (deeper discount) | +$82 gain |
The total return (coupon + capital gain/loss) works out to roughly the same YTM — but the path matters for anyone who has to sell before maturity.
Why Duration Matters More Than Maturity
Maturity tells you when you get your principal back. Duration (specifically Macaulay duration) tells you the weighted-average time you wait for all the bond's cash flows. For a 5-year zero-coupon bond, duration = 5. For a 5-year 5% coupon bond, duration ≈ 4.5 — because you get some money back sooner through the coupons.
The rule of thumb: modified duration estimates how much your bond price will change if yields move by 1%:
A bond with modified duration of 7 will fall roughly 7% in price if yields rise by 1%.
This is why long-duration bonds are risky when rates are rising — and why retirees holding 30-year Treasuries during the 2022 rate hike cycle saw their portfolios crater.
Duration is not the same as maturity. A 30-year bond with a 10% coupon has shorter duration than a 30-year zero-coupon bond — even though both mature in 30 years. Always quote duration when comparing interest-rate sensitivity.
Real Decisions Bond Math Drives
You probably don't trade bonds directly, but the same math governs every fixed-income product:
- CDs (Certificates of Deposit) — A CD is just a single-payment bond. The YTM is the APY the bank quotes.
- Bond funds — ETFs like BND hold hundreds of bonds; the fund's duration is the weighted average.
- Mortgage decisions — when rates rise, your existing mortgage becomes more valuable (you have a below-market rate). When rates fall, consider refinancing.
Try It
Use the Bond Yield Calculator to:
- Solve for YTM on a bond you're considering buying.
- See how a 1% rise in market yields would impact your bond's price.
- Compare a 10-year Treasury vs a 10-year corporate bond at the same YTM — duration differences tell you which carries more rate risk.
The calculator handles annual and semiannual coupons (the US Treasury convention) and shows duration alongside price.